[Lloyd (OP)]

I am thinking about quantum entanglement when I ask the question ... does information have mass?

When I read that pairs or groups of particles can act and react in a way that would indicate they share the same information regardless of their distance apart ... even a cosmic distance apart ... or they receive and act upon the same information instantaneously ... then I have to ask, can information do such a thing when we have a speed limit of C , the speed of light? I guess the answer has to be yes if information has no mass ... and no if information does have mass? Information - distance - spooky action.

[jeffreyH]

Define your interpretation of information.

[Kryptid]

I would say that information as a concept doesn't have mass, but anything that can actually store information will have a mass (at least one associated with its energy via E=mc²). That mass-energy, however, can be arbitrarily small (there is no known upper limit to the wavelength of a photon, except, perhaps, the diameter of the Universe).

[Halc]

When I read that pairs or groups of particles can act and react in a way that would indicate they share the same information regardless of their distance apart ... even a cosmic distance apart ... or they receive and act upon the same information instantaneously ... then I have to ask, can information do such a thing when we have a speed limit of C , the speed of light?

No evidence of this has ever been demonstrated.  In particular, no message (information) has ever been sent at faster than c.
If it did, I'm not sure that would be a demonstration of it having mass or evidence that it cannot have mass.

[evan_au]

Information has entropy associated with it.
Changing information changes the entropy, and this requires energy.
In my simplistic understanding: If some object carries information, it carries energy; this energy has an equivalent mass, and an associated gravitational field.
See: https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory#Negentropy

[Lloyd (OP)]

I read about entangled atoms/electrons transferring information across vast distances ‘instantaneously’ or ‘near-instantaneously’. I also read that the speed of this information transfer was 'around 3-trillion meters per second – or four orders of magnitude faster than light.                   ( https://futurism.com/chinese-physicists-measure-speed-of-quantum-entanglement-2 [nofollow])

My understanding is that anything with mass cannot travel at or beyond the speed of light. My understanding then ... this information shared between atoms/electrons cannot have mass. Hence my question ... does information in this instance have mass ?

[Bored chemist]

Information has entropy associated with it.
Changing information changes the entropy, and this requires energy.
In my simplistic understanding: If some object carries information, it carries energy; this energy has an equivalent mass, and an associated gravitational field.
See: https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory#Negentropy

This leads to a requirement to revisit the joke about the [idiot/ boss/ whatever]  who is seen deleting files from his laptop to make it lighter.

[Halc]

I read about entangled atoms/electrons transferring information across vast distances ‘instantaneously’ or ‘near-instantaneously’. I also read that the speed of this information transfer was 'around 3-trillion meters per second – or four orders of magnitude faster than light.                   ( https://futurism.com/chinese-physicists-measure-speed-of-quantum-entanglement-2)

There is no evidence of actual information transfer with entanglement scenarios.  If there was, it would not have a finite speed (a mere 4 orders of magnitude) as this pop-science article suggests.  Certain interpretations of quantum mechanics posit such information transfer, and also transfer of information arbitrarily far into the past, but without a falsification test, such interpretations cannot be verified.
So the rule of thumb is: If you can't send a message with it, it isn't information transfer, and hence no faster than light information transfer has ever been demonstrated.

My understanding is that anything with mass cannot travel at or beyond the speed of light.

Not even things without proper mass can, according to any theory that holds to the principle of locality.  Said interpretations mentioned above of course must deny this principle.

[jeffreyH]

The sky is blue. That is information about the sky. Does it have mass? No, it is descriptive. The photons have energy, which has an equivalent relativistic mass. Define your interpretation of information.

[Halc]

Information has entropy associated with it.
Changing information changes the entropy, and this requires energy.
...
See: https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory#Negentropy

To expand on this, according to the linked page, the energy is not the mass of the information, but the minimum energy required to save/change a bit of information.  Hence a blank terabyte thumb drive (or say one with the first half set to 0 bits and remainder 1) masses the same as the same thumb drive crammed with a library of findings.  But it takes this minimum energy (and creates the resulting entropy) to change it from one state to the other.

In my simplistic understanding: If some object carries information, it carries energy; this energy has an equivalent mass, and an associated gravitational field.

I don't see how this follows from the linked page, but any object has mass, and mass has energy, so it indeed stands that energy is required to store information in an object.  But it doesn't follow that an object with information masses more than the same object without information (all else being equal). That's a thin statement since a blank thumb drive still has a big consecutive swath of 0's, which is arguably information.

[evan_au]

a blank thumb drive still has a big consecutive swath of 0's, which is arguably information.

One of the definitions of information is "what is the most compact way of representing this data?".
- If there is a more compact way of representing the data, then the data is not 100% information.

In this quote, you summed up 64 GBytes of blank USB drive in just 30 bytes: "a big consecutive swath of 0's".
That demonstrates that the visible* information content of a blank USB is pretty low.


*I know a USB drive has some internal content which is not externally visible, like bad block maps, that does convey information to a blank USB drive...

[Lloyd (OP)]

I will try and define what I mean by information but I think it might just sound silly!

So ... both entangled photons have in their data file/s that the sky is blue.

Now ... what if for some reason only one photon had the data that the sky was blue ... but it wanted the other photon to know the sky was blue? That photon would have to perform an action ... send the data in the form of information to the other photon.

The actual sending of the data then becomes information because it involves an action and has a consequence ... the other photon gains the knowledge that the sky is blue.

But ... now I know a little more about 'entanglement' I'm thinking I couldn't apply my logic to entangled photons because ... they are just that, 'entangled'!

Originally I was imagining one photon at one end of the universe, and one at the other ... one jumping to the left, sending that information to the other, which would jump to the right. I wanted to know if that information that travelled across the universe had matter. If so then it couldn't travel faster than C.

Have you ever dug a big hole ... and then jumped in !? I think I just have !!!

[Halc]

One of the definitions of information is "what is the most compact way of representing this data?".
- If there is a more compact way of representing the data, then the data is not 100% information.

Ouch.  I would say the two words mean the same thing, and if there is a more compact way of representing the data, then the device is not all data. I don't conclude that the data is not all information.

If data/information has mass, then one can get an efficiency measure of a device: the ratio of information mass to total mass. If information has no mass, then this is meaningless as it is always zero. If it is nonzero, is there a theoretical maximum ratio?  If the limit is 1, then a given mass can be pure information.  If the limit is zero (no mass to it), then a different measure is needed, such as bits per joule or something.

In this quote, you summed up 64 GBytes of blank USB drive in just 30 bytes: "a big consecutive swath of 0's".

Hah!  I said I had one of the newfangled 1TB drive. 

That demonstrates that the visible* information content of a blank USB is pretty low

Indeed. The contents of the drive could be crammed into a zip file with only a few bytes.  Not so if filled with white noise. Is that information, or is the library of interesting stuff more information that a terabyte of noise? There are those who say it's all noise until you know how to interpret it, but that's wrong I think. There are language experts that can look at writing or those 'speaking in tongues' and can tell if it has content vs just noise. You can distinguish the information even if you cannot decipher it yet.

I know a USB drive has some internal content which is not externally visible, like bad block maps, that does convey information to a blank USB drive...

Besides the point here. Yes, they have that, but that is part of how it works, not part of the information whose function it is to store.

[Halc]

I will try and define what I mean by information but I think it might just sound silly!

So ... both entangled photons have in their data file/s that the sky is blue.

You can encode that just by sending a blue photon, or rather 420 nm in the frame of the observer. We can send the photons through something that provides alternate paths, thus producing entangled photons so to speak.

Now ... what if for some reason only one photon had the data that the sky was blue ... but it wanted the other photon to know the sky was blue? That photon would have to perform an action ... send the data in the form of information to the other photon.

This borders on anthropomorphism. Photons don't know anything and can't perform actions. They get measured and that's it, and they don't particularly exist until they get measured.  If entangled photons convey 'blue', then I suppose both would have to if measured in a similar manner.

Originally I was imagining one photon at one end of the universe, and one at the other ... one jumping to the left, sending that information to the other, which would jump to the right. I wanted to know if that information that travelled across the universe had matter.

A photon has no position, so it cannot 'jump to the left'.  It only has an eventual measurement.  Nothing you can do to one photon can be used to send information to the other. Information cannot travel faster than light.  So in all the entanglement things you read about, there is no information being exchanged. despite the pop-sci press loving to word it
 that way.  Each measurement takes place, and the time between the two measurements is zero in some frame, and the two measurement are later found to be correlated.  If the two measurements are light years apart, then it will take years to verify the correlation.  No message is sent at superluminal speeds.

[Bored chemist]

Hence a blank terabyte thumb drive (or say one with the first half set to 0 bits and remainder 1) masses the same as the same thumb drive crammed with a library of findings.  But it takes this minimum energy (and creates the resulting entropy) to change it from one state to the other.

Nope.
Absolute entropy exists and there's an energy term associated with it (at any non-zero temperature)

[Halc]

Nope.
Absolute entropy exists and there's an energy term associated with it (at any non-zero temperature)

Not sure which part you're 'Nope'ing. I agree with your statement. There is entropy represented by the thumb drive in any state, and the act of writing information to it (or wiping it) reduces the entropy of the drive, balanced by an increase in external entropy (whatever expended the energy to change the state).
The link Evan provided pretty much discussed a case just like that. It discussed a device in thermal equilibrium getting some of its information changed, thus taking it out of said equilibrium.

[Bored chemist]

Hence a blank terabyte thumb drive (or say one with the first half set to 0 bits and remainder 1) masses the same as the same thumb drive crammed with a library of findings. 

Still nope.

[Halc]

Hence a blank terabyte thumb drive (or say one with the first half set to 0 bits and remainder 1) masses the same as the same thumb drive crammed with a library of findings.

Still nope.

OK, I suppose that needs to be justified.
My justification is that it takes the same energy/effort to write all the zeros at one end and 1's at the other as it does to write them as the contents of a library.  We can say that the initial state of the thumb drive was 'white noise', random bits.

I didn't want it all 0's since lacking implementation details of the thumb drive, I don't know if one state actually entails more mass (say retains electrons) than the other, so I arranged it so that the total number of 1's and 0's is the same in the two cases.

The library has more information.  So does that drive mass more?  You apparently assert that it does, so how would you justify that? I'm not insisting I'm right here. I'm finding this topic interesting and I'm just exploring it.

[Bored chemist]

OK, first thing to check (well- last thing before I go to bed).
Do you agree that a magnet, because it stores energy, weighs more than it did before it was magnetised?
The mass change is tiny but calculable from E=MC^2.

[Halc]

OK, first thing to check (well- last thing before I go to bed).
Do you agree that a magnet, because it stores energy, weighs more than it did before it was magnetised?
The mass change is tiny but calculable from E=MC^2.

Compressing a spring or charging a capacitor definitely stores energy and increases mass accordingly.  A magnet is more tricky since I'm not sure what's involved (adding or removing energy) to put it in that state from a neutral state. I cannot say for sure if a magnet stores energy. It creates a magnetic field, sure, but a gravitational field is effectively negative energy.  An Earth-size mass spread out all over space has little energy, but bring it together into a planet and it has negative potential energy relative to the zero base state. I suspect magnets might be similar, but I'm the worst guy to say that. Not my field at all.

Does it matter?  We're going to be writing the same number of zeros and ones in either case.

Core memory (the old donut bits) https://en.wikipedia.org/wiki/Magnetic-core_memory stored information by spin one way or the other, symmetrical states, neither higher energy than the other.  They sort of dropped that technology about 40 years ago.

So I found this: https://www.explainthatstuff.com/flashmemory.html
The picture in the 'more complex explanation' kind of shows a asymmetrical state where the 1 state stores electrons in the floating gate that are not present in the zero state. There are actually more particles, so 1 has more mass than 0.  So in my example, the total number of 0's and 1's were the same to eliminate this source of there being a difference.

Is the total number of 1's written all at one end of the address space a different mass than the same number of 1's comprising the contents of an encyclopedia written over the address space, or written as just random noise?